What is (2 i - j + k) × ( i + 3 j - 2 k)?

Question 97

MediumOriginal question

What is $(2\hat{i} - \hat{j} + \hat{k}) \times (\hat{i} + 3\hat{j} - 2\hat{k})$ ?

\hat{i} - 5\hat{j} - 7\hat{k}

Correct answerYour answer

-\hat{i} + 5\hat{j} + 7\hat{k}

Correct answerYour answer

-\hat{i} - 5\hat{j} + 7\hat{k}

Correct answerYour answer

2\hat{i} - 3\hat{j} - 2\hat{k}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

Expand $\begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \\ 2 & -1 & 1 \\ 1 & 3 & -2 \end{vmatrix}$ .
$\hat{i}(2 - 3) - \hat{j}(-4 - 1) + \hat{k}(6 + 1) = -\hat{i} + 5\hat{j} + 7\hat{k}$ .

Worth noting

$-\hat{i} - 5\hat{j} + 7\hat{k}$ forgets the minus sign in front of the $\hat{j}$ term.

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